How and when should I start up the system and then when after that should I add tilapia and plants?
You should add plants after you get the system into a starting location and have been running the system for a 3-4 weeks. while adding either raw urine or pure concentrations of ammonia daily to the running water. The ideal is to have the nitrite/nitrate cycle stable before adding fish.
I'm in USDA zone 7a. People are already planting soil gardens here but I'm guessing our night temperatures aren't quite warm enough for tilapia yet.
Depends upon the breed of tilapia. Blue tilapia can easily live in 40+ degree water. They won't grow very quickly but its surviavable.
I've heard various recommendations to get the bacteria going: add chemical ammonia and let it run for a while, add disposable minnows or fish and let it cycle with them for a while, or add pond water which will already contain bacteria. I do have a large, healthy pond on my property with many fish so I have easy access to pond water, minnows, bluegill, crawfish, and tadpoles. I'm ok with losing pond fish as the system balances itself but I'll be buying the tilapia from a supplier so I'd rather have the system stable and safe before I add them. What chemical levels will I need to monitor? What testing kit do I need and where should I get it? Is there a good one on Amazon?
Get the master aquarium testing kit. petco has them and amazon.http://www.amazon.com/API-Freshwater-Master-Test-Kit/dp/B000255NCI/ref=sr_1_1?ie=UTF8&qid=1458229467&sr=8-1&keywords=master+aquarium. test for ammonia, nitrites, nitratesm and PH. If you have hundreds of dollars get the oxygen meter too. http://www.amazon.com/Hanna-Instruments-HI9147-04-Water-Resistant-Aquaculture/dp/B0085X2GZ6/ref=sr_1_2?ie=UTF8&qid=1458229571&sr=8-2&keywords=dissolved+oxygen+meter
What kind of fish food and where should I get it?
Feed your self real food from whole ingrediants and feed the scraps to the fish. NO HOTDOGS. course tilapia will eat almost anything. but the main thing to concentrate on is... are you wanting a heavy harvest of fish?
How many tilapia for this system? I'm hoping to stock them small and then harvest them at the end of the growing season.
Well, thats a 300 gallon system tank. A realatively safe level would be if you stock for aprox 1 pound of fish per 5 gallons of water. 60 pounds of fish at the end of the season, depending on growth.
What easy to grow, hard to kill plants would you recommend for a beginner in zone 7a? We like full-sized tomatoes, jalapeño peppers, poblano peppers, zucchini, strawberries, and squash if they're not to difficult. If they are I'll probably skip them for the first year. I'm open to suggestions on whatever's easy!
The fruiting stuff will need a couple ounces of phosphorus and potassium added to the media beds. you should consider dual-root zone aquaponics. It allows for amendments to be added to the root zone of the plant instead of indiscriminately to the system.
The person I got the system from ran it without any aeration aside from the natural splashing as water runs into the growbeds, fish tanks, and sump tanks. Think I'll be ok with this or should I add an aerator?
You will be ok like this most likely... But growth of tilapia follows the 1-1-1 guideline. 1 pound of feed plus 1 pound of oxygen grown for 1 year equals 1 pound. More oxygen will allow the quick growth that your interested in.